Theorem e022

Description: A virtual deduction elimination rule. (Contributed by Alan Sare, 24-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	e022.1	⊢ 𝜑
	e022.2	⊢ (    𝜓    ,    𝜒    ▶    𝜃    )
	e022.3	⊢ (    𝜓    ,    𝜒    ▶    𝜏    )
	e022.4	⊢ ( 𝜑 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
Assertion	e022	⊢ (    𝜓    ,    𝜒    ▶    𝜂    )

Proof

Step	Hyp	Ref	Expression
1		e022.1	⊢ 𝜑
2		e022.2	⊢ (    𝜓    ,    𝜒    ▶    𝜃    )
3		e022.3	⊢ (    𝜓    ,    𝜒    ▶    𝜏    )
4		e022.4	⊢ ( 𝜑 → ( 𝜃 → ( 𝜏 → 𝜂 ) ) )
5	1	vd02	⊢ (    𝜓    ,    𝜒    ▶    𝜑    )
6	5 2 3 4	e222	⊢ (    𝜓    ,    𝜒    ▶    𝜂    )